South Korean President Park Geun-hye bows her head as she apologises for the crisis caused by the alleged influence of her old friend Choi Soon-sil.
Photograph: YONHAP/EPA

South Korean president Park Geun-hye’s has made a tearful apology for her role in a “heartbreaking” political scandal that has engulfed her administration – but it has failed to mollify opposition parties.

In a televised address on Friday, Park said she would cooperate with prosecutors in their investigation into allegations that she allowed Choi Soon-sil, a friend of 40 years, to influence government policies on everything from the economy to North Korea.

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But soon after Park’s apology – her second in 10 days – the leader of South Korea’s main opposition party accused her of “insincerity” and of desperately clinging to power.

“She does not seem to understand the gravity of the whole situation,” said Choo Mi-ae, leader of Democratic Party of Korea. “She is only interested in maintaining her grip on power.

“The president should remove her hands from state affairs.”

Earlier, in a brief televised address to journalists, Park said that prosecutors should clarify what happened and that everyone involved, including herself, should be held accountable and take responsibility if found guilty.

It is not clear what action could be taken against Park, as South Korea’s constitution does not allow a sitting president to be prosecuted.

“These latest developments are all my fault and were caused by my carelessness,” she said, adding that she had “allowed my guard to drop” around Choi.

“It is hard to forgive myself and sleep at night because of the feelings of sorrow,” Park said, her voice trembling.

Choi is alleged to have used her closeness to the president to meddle in state affairs, and her lawyer has said he expects prosecutors to look into whether she inappropriately received classified documents. Choi has also been accused of using her ties to Park to benefit unlawfully from two non-profit organisations.

“It is very miserable and regrettable that a particular individual is said to have taken profits and committed several unlawful acts, while we are working on a job in hopes of helping the national economy and people’s lives,” Park said, referring to Choi.

However, Park denied some of the more lurid rumours surrounding the scandal - including reports that she had fallen into a religious cult and conducted shamanist rituals in the presidential Blue House.

The scandal has triggered a media frenzy with fresh reports – many of them highly speculative and unsubstantiated – emerging every day, tying Choi and some of her extended family members to more alleged malpractices.

Some reports have also suggested that Choi was still involved in marginal religious group created by her father and that Park had fallen under its influence.

“There have been claims that I fell for a religious cult or had (shamanist rituals) performed in the Blue House, but I would like to clarify that those are absolutely not true,” Park said in her address.

Opposition parties have stepped up their criticism of Park, who has just over a year of her term to run, but have stopped short of calling for her resignation. That would trigger an early presidential election that they would not be confident of winning.

But South Korean media reports said that if her choice of prime minister, Kim Byong-joon, is rejected and she is forced to name someone chosen by the opposition, she will effectively become a lame duck president.

At best, Park will limp on to the end of her term with her power severely undermined at a time of slowing economic growth, rising unemployment and tensions with North Korea.